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**Solving Op Amp Stability Issues Part 4**

This presentation will focus on techniques to solve voltage feedback op amp stability problems. The content is intended to teach any range of professional, from technician to PHD, to become an op amp stability expert! (For Voltage Feedback Op Amps) Tim Green & Collin Wells Precision Analog Linear Applications

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**10) Noise Gain and CF (Output Cload)**

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**Noise Gain and CF: Programmable Power Supply (PPS) Design Example**

Define min and max load condition Design for: 250nA< Iout <2A Cload = 10μF Check for stability at Iout range DC and Transient Analysis Circuit

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**Original Transient Analysis**

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**Noise Gain and CF Compensation Design Steps**

Define min and max load condition SPICE simulation for Loaded Aol curves (min and max load) Plot Desired 1/b on Loaded Aol curves (min and max load) A) Use Noise Gain and CF Compensation 4) From Desired 1/b detemine fp3, fp4, and Mid-Band Gain 5) Compute values for RF, CF, Rn, Cn based on plotted fp3, fp4, Mid-Band Gain 6) SPICE simulation w/final compensation for Loop Gain (Aolb) Magnitude and Phase 7) Adjust Compensation if greater Loop Gain (Aolb) phase margin desired 8) Check closed loop AC response for VOUT/VIN Look for peaking which indicates marginal stability Check if closed AC response is acceptable for end application 9) Check Transient response for VOUT/VIN A) Overshoot and ringing in the time domain indicates marginal stability The CF Compensation design steps are outlined here. Rules-of-thumb will be present to yield best stability on first pass analysis.

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**2) Loop Gain Check for Loaded Aol**

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**2),3),4) Loaded Aol and Desired 1/β**

On Loaded Aol Curves add Desired 1/β: Noise Gain & CF Compensation fp3=336Hz fp4=10.6kHz Mid-Band Gain = 30dB 1) Loaded Aol_A Curve: fp1_A is low frequency pole from op amp unloaded Aol down around 1Hz. fp2_A is second pole in Loaded Aol_A due to Zo and CLoad. 2) Loaded Aol_B Curve: fp1_B is low frequency pole in Loaded Aol due to lower resistive loading of 1.25 ohms on CMOS output. fp2_B is second pole in Loaded Aol_A due to Zo and CLoad. 3) Desired 1/β Curve: fz1 and fp3 are a zero and pole due t noise gain set by Rn and Cn. We do not need to know exact location of fz1 since once we set fp3, fz1 can be seen graphically by using a +20dB/decade slope from fp3 down in frequency to the DC gain of 0dB. Noise gain fp3 is easy to find and compute. fp4 is due to CF. fz1 is the result of high frequency 1/β going to 0dB due to CF acting as a short at high frequencies. All we need from our drawn, Desired 1/β curve is fp3, Mid-Band Gain and fp4. The other 1/β zeroes will occur as plotted by the nature of the input and feedback networks containing only one reactive element. General considerations: Because of the large difference between the two loaded Aol curves at high frequency it is necessary to plot the Desired 1/β as the best compromise to keep most phase margin for the two cases. This is shown here. We will strive for better than 45 degrees phase margin for each case to allow for Aol shifts in the real world. A worst case Aol frequency shift at the Unity Gain Bandwidth (UGBW), over process and temperature, can be estimated as ½*UGBW to 1.5*UGBW. For best “Phase Buffer” we prefer to keep fp3 and fz1 one decade apart. We cannot quite do that here so we compromise as shown.

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**5) Noise Gain and CF Compensation**

Noise Gain & CF Compensation fp3=336Hz fp4=10.6kHz Mid-Band Gain = 30dB Loop Gain (Aolβ), Loaded Aol, 1/ β Circuit

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**5) Final Compensation: 1/β & Loaded Aol**

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**6) Final Compensation: Loop Gain (Aolβ)**

Phase Margin Phase Margin

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**7) Final Compensation: Vout/Vin AC Closed Loop**

Note for Non-Inverting Noise Gain Compensation: Rsource < 1/10*Rn OR 2) Add capacitor (>10*Cn) at U1, +input, to ground to lower impedance to < 1/10*Rn at fp3 for effective Non-Inverting Noise Gain Compensation Vout/Vin AC Closed Loop and Transient Circuit

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**8) Final Compensation: Vout/Vin AC Closed Loop**

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**9) Final Compensation: Transient Analysis**

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**11) Output Pin Compensation (Output Cload)**

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**Output Pin Compensation – Design Example**

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**INA152 Transient Analysis – No Compensation**

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**Aol Test Circuit for Difference Amp**

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INA152 Aol

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INA152 Aol

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**Output Pin Compensation Design Steps**

SPICE simulation for Loaded Aol curves (min and max load) Measure Zo in SPICE 3) Determine if CLoad is on resistive portion of Zo 4) Plot Loaded Aol Original and Loaded Aol New for Ouptut Pin Compensation 5) Compute Rco and Cco and check Loaded Aol New in SPICE 6) SPICE simulation w/final compensation for Loop Gain (Aolb) Magnitude and Phase 7) Adjust Compensation if greater Loop Gain (Aolb) phase margin desired 8) Check closed loop AC response for VOUT/VIN Look for peaking which indicates marginal stability Check if closed AC response is acceptable for end application 9) Check Transient response for VOUT/VIN A) Overshoot and ringing in the time domain indicates marginal stability The CF Compensation design steps are outlined here. Rules-of-thumb will be present to yield best stability on first pass analysis.

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1) INA152 Loaded Aol

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1) INA152 Loaded Aol

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2) INA152 ZO Test

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**2) TINA SPICE ZO Test Circuit**

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2) INA152 ZO Magnitude

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2) INA152 ZO Pole and Zero

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**3) INA152 ZO and CL Note : For both capacitive values of CL**

the load impedance interacts with Zo in its “high frequency” Zo resistive region (Zo_Hif).

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**4) INA152 Loaded Aol: Original and New**

Add Cco = 10x CL then fp3 will move one decade to the left of fp2 Add Rco to create fz1 Keep fz1 < 10*fp3 for overall best loop gain phase margin

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**5) Compute Rco and Cco Not seen by Output Pin Compensation**

Loaded Aol New

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**5) Compute Rco and Cco and check in SPICE**

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**5) Compute Rco and Cco and check in SPICE**

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6),7) Loop Gain Check

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6),7) Loop Gain Check Loop Gain Phase Margin = 47 degrees

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**8) Closed Loop AC Response**

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**8) Closed Loop AC Response**

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9) Transient Analysis

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9) Transient Analysis

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**9) Transient Analysis Zoom on VOUT Zoom on VOUT Rising Edge**

Falling Edge

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**12) Riso with Dual Feedback (Output Cload) - Zo, 1/b, Aol Technique**

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**Riso with Dual Feedback- Zo, 1/b, Aol Technique**

1) Given: Op Amp and Cload 2) Determine Op Amp Zo Measure in SPICE OR Data Sheet Curve 3) Create External Zo Model for Loop Gain Analysis only 4) If large RF value to be used model Cin_eq 4) Set Riso = 1/10*Ro 1/β_Hif ≈ 20dB 5) SPICE simulation: Aol, 1/β FB#1 A) FB#1 gives: 1/β_Lof and fz1 6) Draw 1/β FB#2 (1/β_Hif ≈ 20dB from Step 4) A) fp1=10*fz1 B) fz3=1/10*fp1 C) fp1<1/10*fcl 7) Choose RF and CF so standard values yield fz3 8) SPICE simulation: Loop Gain (Aolβ) Magnitude & Phase A) Adjust compensation for more Loop Gain (Aolβ) phase margin if needed 9) Check closed loop AC response for VOUT/VIN A) Look for peaking which indicates marginal stability B) Check if closed AC response is acceptable for end application 10) Check Transient response for VOUT/VIN A) Overshoot and ringing in the time domain indicates marginal stability The Riso Compensation design steps are outlined here. Two cases, Case A and Case B, will be presented. Rules-of-thumb will be presented to yield best stability on first pass analysis.

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**1) Riso w/Dual Feedback Dual Feedback:**

FB#1 through RF forces accurate Vout across CL FB#2 through CF dominates at high frequency for stability Riso provides isolation between FB#1 and FB#2

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**2) OPA177 Zo – SPICE Measurement**

For many op amp application circuits is will be necessary to know the op amp Open Loop Small Signal AC Output Impedance, Zo. Often this can be obtained from the op amp data sheet. Many op amp SPICE macromodels properly model Zo. If the data sheet contains a Zo curve we can easily check the macromodel for Zo accuracy. The test circuit here uses inductor, LT, in the feedback path to act as a short for the DC Operating Point analysis. The capacitor, CT, on the –input to ground is open for DC Analysis and will be a short for all frequencies of interest during the AC Analysis. Current Generator, IG1, is set to DC Current =0 and selected as AC Current of 1. During the AC Analysis IG1 injects current into the output, Vout, and the op amp is open loop. AC Analysis reports Vout in dB over frequency as a ratio of Vout/IG1 which is Zo, in dB. To convert Zo in dB to Zo in ohms simply change the y-axis scaling from dB-Linear to logarithmic.

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**3) Riso w/Dual Feedback – Zo External Model**

VCVS1 ideally isolates U1 so U1 only provides data sheet Aol at VOA Set Ro to match measured Ro Analyze with unloaded Ro (largest Ro) which creates worst instability Use 1/β on Aol stability analysis 1/ β, taken from VOA, will include the effects of Zo, Riso, and CL

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**3) Zo External Model, FB#1 and FB#2 Analysis**

There is only one net voltage fed back as β to the –input of the op amp β_net = β_FB#1 + β_FB#2 This implies that the largest β will dominate → smallest 1/ β will dominate Analyze FB#1 with CF = open since it will only dominate at high frequencies Analyze FB#2 with CL = short since it is at least 10x CF

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**4) OPA177 Input Capacitance**

**************************** * OPA177 "E" - ENHANCEMENTS * OUTPUT SUPPLY MIRROR FQ POLY(1) VLIM 0 1 DQ DX DQ DX VQ VQ FQ POLY(1) VQ E-3 1 FQ POLY(1) VQ E-3 -1 * QUIESCIENT CURRENT RQ E4 * DIFF INPUT CAPACITANCE CDIF E-12 * COMMON MODE INPUT CAPACITANCE C1CM E-12 C2CM E-12 OPA177 Input Capacitance: Ccm- and Ccm+ are common mode input capacitance Cdiff is differential input capacitance Ccm and Cdiff can usually be found in op amp data sheet For OPA177 Ccm and Cdiff are found inside the SPICE macromodel

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**4) Cin_eq Equivalent Input Capacitance for Loop Gain Analysis**

Input Capacitance and Loop Gain Analysis: Final Loop Gain circuit break needs to break both FB#1 and FB#2 Loop Gain circuit break will need to be made on op amp –input For some op amps feedback elements can interact with input capacitance and add zero or pole to 1/β For Loop Gain analysis break loop at –input but add Cin_eq

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5) 1/β FB#1 Analysis Set Riso = 1/10*Ro 1/β_Hif ≈ 20dB

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5) 1/β FB#1 SPICE Results C TINA SPICE Post Processing Math Anomaly

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**6) Add FB#2: Draw Desired 1/β FB#2on Aol & 1/β FB#1 Curves**

Set Riso = 1/10*Ro 1/β_Hif ≈ 20dB

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**7) 1/β FB#2 Analysis For 1/β FB#2 SPICE Analysis: Set Vref = 0V**

Else OPA177 VOA will saturate with Vout = 5V into a short Set Riso = 1/10*Ro 1/β_Hif ≈ 20dB

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7) 1/β FB#2 SPICE Results

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7) SPICE 1/β Complete

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**8) SPICE Loop Gain Complete**

Phase Margin = 82 degrees

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9) SPICE AC Closed Loop

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9) SPICE AC Closed Loop

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**10) SPICE Transient Analysis**

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**13) Discrete Difference Amplifier (Output Cload)**

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**Difference Amp w/CLoad: No Compensation**

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**Difference Amp w/CLoad: No Compensation**

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**Discrete Difference Amplifier Compensation Design Steps**

SPICE simulation for Loaded Aol curves Plot Desired 1/b on Loaded Aol curves A) Use Noise Gain Compensation 3) From Desired 1/b determine fp and 1/β_Hif 4) Compute values for Rn, Cn based on fp and 1/β_Hif 5) SPICE simulation w/final compensation for Loop Gain (Aolb) Magnitude and Phase Adjust Compensation if greater Loop Gain (Aolb) phase margin desired 7) Add Rnp-Cnp to +input of Difference Amplifier for flat VOUT/VIN Response Look for peaking which indicates marginal stability Check if closed AC response is acceptable for end application 8) Check Transient response for VOUT/VIN A) Overshoot and ringing in the time domain indicates marginal stability The CF Compensation design steps are outlined here. Rules-of-thumb will be present to yield best stability on first pass analysis.

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**1) Loaded Aol: No Compensation**

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**1) Loaded Aol: No Compensation**

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2), 3) Plot 1/β on Loaded Aol

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4) Compute Rn and Cn

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5),6) Loop Gain Check Loop Gain Phase Margin = 81 degrees

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**7) VOUT/Vin_diff: Noise Gain Compensation**

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**7) VOUT/Vin_diff: Noise Gain Compensation**

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**7) Rnp-Cnp Compensation plus Noise Gain Compensation = FLAT VOUT/Vin_diff Response**

Add Rnp-Cnp Compensation: Rnp = Rn Cnp = Cp This will balance the differential gain so inverting and non-inverting gain paths have the same gain over frequency for a flat differential gain of VOUT/Vin_diff. No Effect on Loop Gain (Aolβ)

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**7) Rnp-Cnp Compensation plus Noise Gain Compensation = FLAT VOUT/Vin_diff Response**

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**7) Rnp-Cnp Compensation plus Noise Gain Compensation = Improved CMRR**

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**7) Rnp-Cnp Compensation plus Noise Gain Compensation = Improved CMRR**

OPA2367 CMRR = 600kHz Difference Amp Noise Gain Compensation Rnp-Cnp Compensation CMRR = 600kHz

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**7) Rnp-Cnp Compensation plus Noise Gain Compensation = Improved CMRR**

Difference Amp Noise Gain Compensation Rnp-Cnp Compensation CMRR = 600kHz OPA2367 CMRR = 600kHz

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**8) Transient Analysis: Rnp-Cnp Compensation plus Noise Gain Compensation**

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**8) Transient Analysis: Rnp-Cnp Compensation plus Noise Gain Compensation**

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